Nonunique steady states in the disordered harmonic chain

The heat transport in disordered harmonic chains (DHCs) with arbitrary heat baths is studied, based on a general formulation developed by Dhar [Phys. Rev. Lett. 86, 5882 (2001)]. The obtained temperature profile of a steady state is very unusual for any heat bath: (i) it is not unique, but dependent on the initial condition; (ii) it may be highly nonlinear, even though the temperature difference of the two ends of the system is in zero limit, and the temperature gradient ∇T is not inversely proportional to the system size; and (iii) when a DHC is coupled to two thermostats with the same temperature, the temperature of the system is still not uniform. The localized higher frequency normal modes induced by the mass disorders are responsible for these strange properties.